5 minutes is too long. My Debian systems never demand that I update them. When I update them, it never even takes two minutes.

That can't be helped. I go for a smoke and when come back system is already upgraded.

I've not being using Debian setups lately, but on Ubuntu, alert on need-to-reboot packages after daily unattended upgrades run is happening almost every month. I'm kinda sure that Debian is on similar schedule here.